1. Texture Synthesis over Arbitrary Manifold Surfaces Li-Yi Wei Marc Levoy Computer Graphics Group Stanford University

2. Introduction + Synthesize a surface texture by coloring mesh vertices Input TextureInput MeshResult

3. Desirable Properties Share advantages of 2D algorithm [SIGGRAPH 2000] –Quality –Efficient –General –Easy to use Minimum distortion Minimum discontinuity

4. Previous Work Texture Mapping –Global [Catmull’74, Bier’86, Levy’98] –Local Triangle tiles [Neyret’99] Lapped textures [Praun’00]

5. Previous Work 3D Texture synthesis –procedural [Perlin’85, Turk’91, Witkin’91] –from example surface texture [Gagalowicz’86, Turk’01, Ying’01] volume texture [Heeger’95, Ghazanfarpour ’96]

6. Previous Work 2D Texture from Example –pyramid matching [Heeger’95, Simoncelli’98] –block shuffling [De Bonet’97, Xu’00] –Markov Random Field [Popat’93] –neighborhood search [Efros’99, Wei’00]

7. Texture Synthesis by Neighborhood Search noise Input pyramid noise Output pyramid Search Copy

8. Surface Texture Synthesis by Neighborhood Search Input pyramid Output pyramid Search

9. Differences between Images and Meshes Our Solution image mesh Synthesis Order Pixels/Vertices Local Orientation (Vector field) ? ? mesh re-tiling [Turk’92] user-specified relaxation random scanline u v grid Neighborhood flattening/resampling normal ? ? tangent bitangent

10. Process 1. Build image/mesh pyramids 2. Assign texture orientation 3. Generate texture

11. Image & Mesh Pyramids Mesh Retiling [Turk’92]

12. Retiling Density 24576 vertices73728 vertices

13. Texture Orientation Methods for orienting textures –user-specified –random (for isotropic textures) –smooth or symmetric (for anisotropic textures) by relaxation

14. 4-way symmetric texture 4-way symmetric vector field Texture Orientation

15. Texture Orientation by Relaxation Minimize an error function –similar to [Hertzmann’00, Pedersen’95]

16. Synthesis

17. Synthesis : 2 Lowest Levels

18. Synthesis : Lowest Level Random copy

19. Synthesis Pass1 : Extrapolation Search Copy Shooting normal

20. Synthesis Pass2 : Full Neighborhood Search Copy

21. Neighborhood Comparison compare ?

22. Mesh Neighborhood Resample Compare Resampled Grid 2D Patch 3D Patch Flatten (Maillot’93)

23. Accelerating Neighborhood Search Tree-structured Vector Quantization [Wei’00]

24. Multiresolution Synthesis

25. Results: Random Orientation

26. Results: Other Orientations RandomUser-specified Relaxation 2-way symmetry 4-way symmetry

27. Results smooth4-way symmetryrandom

28. Results Surface displacement smooth2-way symmetry

29. Summary of Differences Turk’s approachOur approach Vector field Traversal order Neighborhood Mesh hierarchy smoothrandom, symmetric sweepingrandom surface marchingflattening/resampling explicit parent/childshooting normal

30. Future Work Texture transfer between models Texturing animated models Mesh signal processing

31. More Information http://graphics.stanford.edu/projects/texture/

33. Texture Orientation Examples Random4-way symmetric2-way symmetric

34. Synthesis Order ScanlineRandom Input

35. Differences between Turk’01 and Our Approach Turk’s approach Our approach Vector field Traversal order Neighborhood Mesh hierarchy smooth random, symmetric sweepingrandom surface marchingflattening + resampling explicit parent/childshooting normal

40. Introduction Texture Synthesis Input Result

41. Introduction + Synthesize a surface texture by coloring mesh vertices Input TextureInput Mesh Result Synthesis

42. Previous Work Synthesis from Example General Applicable to surfaces Low distortion No discontinuity Texture mapping Lapped textures Efficient Procedural texturing

43. Image Texture Synthesis Exhaustively search neighborhoods

44. Image Texture Synthesis

45. Mesh Pyramid Mesh Retiling: Turk’92

46. Key Idea Reuse the neighborhood-search framework Output pyramid Input pyramid Search

47. Key Idea Reuse the neighborhood-matching framework

48. Synthesis Lowest Level Random copy

49. Synthesis : Pass1 Copy Search Shooting normal

50. Synthesis : Pass2 Search Copy

51. Neighborhood Comparison Compare ?

52. Mesh Neighborhood 3D Patch

53. Mesh Neighborhood Resample Compare 3D Patch 2D Patch Resampled Grid Flatten (Maillot’93)

54. Synthesis : Pass1 Random copy Copy Search Shooting normal

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